A few Calculus problems.

I have been working on my AP Calculus homework, and there are a few things I can't understand. Can you help? These are three, seperate, unrelated problems.

1) I need to graph and explain the graph of ln(ln(x))

2) For the graph of the function of f, where x = # of DVDs produced and y = Cost of production, what does f^-1(10) represent? (That's f-inverse(10), I wasn't sure if the way I typed it was correct or not.)

3) I was given the inverse function of F. Do I get F using the same method I would to get inverse of F only go the other way around? and is finding the F function how I should be finding f(1)?

If anybody helps, I really appreciate it. And I'm not specifically looking for answers, I would like an explanation of how to do the problems. I like knowing how and why instead of what the answer is. Thanks again!

I have been working on my AP Calculus homework, and there are a few things I can't understand. Can you help? These are three, seperate, unrelated problems.

1) I need to graph and explain the graph of ln(ln(x))

so what have you done here? note that the domain of the graph would be $\displaystyle (1, \infty)$. why? and it will be in a somewhat similar in shape to ln(x) but it would increase less steeply. why?

2) For the graph of the function of f, where x = # of DVDs produced and y = f(x) = Cost of production, what does f^-1(10) represent? (That's f-inverse(10), I wasn't sure if the way I typed it was correct or not.)

do you understand the relationship between a function and its inverse?

I have been working on my AP Calculus homework, and there are a few things I can't understand. Can you help? These are three, seperate, unrelated problems.

1) I need to graph and explain the graph of ln(ln(x))

Have you graphed it? Remember that it is not saying ln(x) times ln(x), this is a composite function, ie. f(g(x)) so you are evaluating ln(x) IN TERMS OF ln(x). This is a really cool question and I think if you look at the graph of this function for awhile you can come up with a good answer. Hint: Remember that a log is just an exponent. These kinds of questions are supposed to make you think, not get an answer from someone on a help forum. If you are in AP Calculus, you didn't get there by accident

2) For the graph of the function of f, where x = # of DVDs produced and y = Cost of production, what does $\displaystyle f^{-1}(10)$ represent?

Typically, the inverse of a cost vs. production graph, is the price per unit of what ever is being produced. Cost of production increases as more units must be produced; the more units they can sell means the lower the price of each unit can be. $\displaystyle f^{-1} (10)$ is asking you what is happening on the inverse graph of f(x) at x=10.

3) I was given the inverse function of F. Do I get F using the same method I would to get inverse of F only go the other way around? and is finding the F function how I should be finding f(1)?

If f is the inverse of g, then g is the inverse of f. This is an elementary property of inverse functions.

If anybody helps, I really appreciate it. And I'm not specifically looking for answers, I would like an explanation of how to do the problems. I like knowing how and why instead of what the answer is. Thanks again!